Minimal Models of Integrable Lattice Theory and Truncated Functional Equations

TL;DR

This paper introduces minimal models of integrable lattice theory derived from the XXZ model with special boundary conditions, utilizing Quantum Group reduction at roots of unity to derive truncated functional equations.

Contribution

It demonstrates how Quantum Group reduction leads to closed truncated functional relations for Sklyanin's transfer-matrices in minimal models.

Findings

Sklyanin's transfer-matrices satisfy truncated functional relations

Explicit solutions provided for the simplest case

Establishes a link between Quantum Group reduction and minimal models

Abstract

We consider the integrable XXZ model with the special open boundary conditions. We perform Quantum Group reduction of this model in roots of unity and use it for the definition Minimal Models of Interable lattice theory. It is shown that after this Quantum Group reduction Sklyanin's transfer-matrices satisfy the closed system of the truncated functional relations. We solve these equations for the simplest case.